1. Field of the Invention
The invention relates to magnetic field generating apparatus particularly for use in performing a nuclear magnetic resonance (NMR) experiment.
2. Description of the Prior Art
NMR experiments rely on placing a sample to be examined in a controlled magnetic field, generally having a high homogeneity. MRI magnets have been designed to produce spherical zones of homogeneity by cancelling between axial coil arrays low error order terms, say Z2 and Z4, and as many higher order terms as permitted by cost constraints. It is well known that an array of n axial coils will correct up to 2n axial even orders--ie. a four coil magnet corrects Z.sub.2, Z.sub.4, Z.sub.6 (there are always considered an even number of coils symmetrically placed about the midplane of the magnet). The diameter of the homogeneous zone increases as higher orders are cancelled, but it becomes more costly to do this as more coils are needed. Now it happens, that the higher order terms contribute to the net field at a radial point more strongly as the radius of the homogeneous zone increases. Another way of looking at this is to say that as the considered field point is moved out in radius, closer to the inner radius of the coils, the local field contribution of the nearest coil dominates the situation, increasing the rate of field charge with radius. Therefore, it is usual to accept that MRI magnets, comprised of a few discrete coils are designed to produce ussable homogeneity over, perhaps half of their bore diameter. It is too costly to correct a large number of high orders by discrete arrays. As the maximum diameter of the object subjected to NMR is increased, the magnet bore size has to be increased such that the magnet bore diameter is twice the maximum subject diameter.
Increasing the diameter of the coil set is costly in superconductor. The following simple analysis shows that for fixed field and conductor hoop stress, cost rises in proportion to the radius cubed.
V=2.pi.a A n, a=coil radius, A=coil cross-section, n=nos turns PA1 Bo=.mu.o*n*I/a, for a simple coil Substituting for I PA1 Cost=(2.pi./.mu.)*a.sup.3 *Bo.sup.2 /.sigma.
Stress in a turn .sigma.=I*Bz*a/A. I=current, Bz is local axial field .sigma.=I*a*Bo/A,Bo-Bz where Bo is the bore field
Conventional MRI magnets are not satisfactory, therefore, for examining relatively large objects where the areas of interest extend beyond the region which can be placed within the spherical homogeneous region even though the object can be placed within the coils.